Answer:
B. x= 7
Step-by-step explanation:
6x = 42
x = 42 / 6
x = 7
The 6 is multiplying because of the x, this passes to the other side of the equal to split.
PLLLLLZ HELP I HAVE A DEADLINE Write a recursive formula for finding the nth term of each arithmetic sequence. 15.75, 14.25, 12.75, …
a1 = 15.75, an = an – 1 + 1.5
a1 = 12.75, an = an – 1 – 1.5
a1 = 11.25, an = an – 1 + 1.5
a1 = 15.75, an = an – 1 – 1.5
Answer: D. a1=15.75,an = an -1 -1.5
Step-by-step explanation:
Sorry about the no explanation, but the answer is correct.
The correct recursive formula for the arithmetic sequence 15.75, 14.25, 12.75, … is a1 = 15.75, an = an-1 - 1.5. This means the first term is 15.75 and each following term is 1.5 less than the previous term.
Explanation:The question asks for a recursive formula for the arithmetic sequence provided. An arithmetic sequence is a sequence of numbers wherein the difference between any two consecutive terms is constant. In this case, the common difference (d) is -1.5, because each term decreases by 1.5 from the previous term. Every term in the sequence follows the pattern of the first term, plus the common difference (d) multiplied by (n-1), where n is the term number.
To write a recursive formula for the sequence, we express the nth term (an) as the sum of the (n-1)th term and the common difference. Thus, the recursive formula for the sequence is: a1 = 15.75, an = an-1 - 1.5. This tells us that the first term a1 equals 15.75, and any term an (after the first term) is 1.5 less than the term before it(an - 1).
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A shade of paint is made by evenly mixing m gallons of white paint, costing $12 a gallon, with n gallons of blue paint, costing $30. What is the cost, in dollars per gallon, of the resulting mixture?
Answer:
The cost of mixture is
[tex]\dfrac{12m + 30n}{m+n}\text{ dollars per gallon}[/tex]
Step-by-step explanation:
We are given the following in the question:
Cost of white per gallon = $12 a gallon
Amount of white paint in the mixture = m gallons
Total cost of white paint =
[tex]12\times m = 12m\$[/tex]
Cost of blue per gallon = $30 a gallon
Amount of blue paint in the mixture = n gallons
Total cost of blue paint =
[tex]30\times n = 30n\$[/tex]
Total cost of mixture =
Total cost of white paint + Total cost of blue paint
[tex](12m + 30n)\text{ dollars}[/tex]
Total amount of mixture =
Amount of white paint in the mixture + Amount of blue paint in the mixture
[tex]=(m+n)\text{ gallons}[/tex]
Cost of mixture per gallon =
[tex]=\dfrac{\text{Total cost}}{\text{Total amount}}\\\\=\dfrac{12m + 30n}{m+n}\text{ dollars per gallon}[/tex]
is the required cost of mixture.
Carl and rick are traveling to a store 5 miles away. Carl is riding a bike, so he's going 12 mph faster than rick. If it takes rick 45 minutes, how long it take carl?
Answer:
Therefore Carl takes[tex]=16.07 mins[/tex]
Step-by-step explanation:
Speed : speed is the ratio of distance to time.
[tex]speed=\frac{distance}{time}[/tex]
The S.I unit of speed = m/s
The C.G.S unit of speed = cm/s
12 mph means 12 miles per hour.
Let the speed of Carl be x.
Carl is going 12mph faster than Rick.
Then the speed of Rick is = (x-12)mph
We know that,
[tex]time =\frac{distance}{speed}[/tex]
[tex]Time =\frac{5}{x-12}[/tex] h
45 minutes = [tex]\frac{45}{60}[/tex] h
According to the problem,
[tex]\frac{5}{x-12} =\frac{45}{60}[/tex]
[tex]\Rightarrow 45(x-12)=5\times60[/tex]
[tex]\Rightarrow45x-540 = 300[/tex]
[tex]\Rightarrow 45x=300+540[/tex]
[tex]\Rightarrow x=\frac{840}{45}[/tex]
We know that,
[tex]time =\frac{distance}{speed}[/tex]
Therefore Carl takes [tex]=\frac{5}{\frac{840}{45} } h[/tex] [tex]=\frac{5\times 45\times 60}{840} mins[/tex] [tex]=16.07 mins[/tex]
Carl will take approximately 16.08 minutes to travel the 5 miles to the store.
Step 1:
Determine Rick's speed.
Since Rick travels 5 miles in 45 minutes, we first convert 45 minutes to hours: 45 minutes ÷ 60 minutes/hour = 0.75 hours. Then, we find Rick's speed: Speed = Distance ÷ Time = 5 miles ÷ 0.75 hours = 6.67 mph.
Step 2:
Determine Carl's speed.
Since Carl is riding a bike 12 mph faster than Rick, we add 12 mph to Rick's speed to find Carl's speed: Carl's speed = Rick's speed + 12 mph = 6.67 mph + 12 mph = 18.67 mph.
Step 3:
Calculate Carl's time.
Now that we know Carl's speed, we can calculate how long it will take him to travel 5 miles. Time = Distance ÷ Speed = 5 miles ÷ 18.67 mph ≈ 0.268 hours.
Step 4:
Convert Carl's time to minutes.
To convert hours to minutes, we multiply by 60: 0.268 hours × 60 minutes/hour ≈ 16.08 minutes.
Step 5:
Interpret the result.
It will take Carl approximately 16.08 minutes to travel 5 miles to the store.
2/3 of the students study a language 2/5 of the students study french Find the ratio of students who study french to students who do not study french.
Answer:
Therefore the ratio of students who study french to students who do not study french is 4:11.
Step-by-step explanation:
Given that [tex]\frac2 3[/tex] of the students study a language. [tex]\frac2 5[/tex] of the students study french.
Consider total number of student be x.
The number of student who study language [tex]= \frac2 3\times x[/tex]
Again [tex]\frac2 5[/tex] of the students study french.
The number of student who study french [tex]= \frac2 3\times x\times \frac25[/tex]
[tex]=\frac{4}{15}x[/tex]
The number of student who do not study french
[tex]=x-\frac{4}{15}x[/tex]
[tex]=\frac{x(15-4)}{15}[/tex]
[tex]=\frac{11x}{15}[/tex]
Therefore the ratio of students who study french to students who do not study french is
[tex]=\frac{4}{15}x:\frac{11}{15}x[/tex]
=4:11
Answer:
(2/3)(300)= 200, study a language. Of those, 2/5, so (2/5)(200)= 80, study French. The other 300- 80= 220 students do not study French. The ratio of students who study French to those who do not is 80 to 220 which can be reduced to 8 to 22 and then 4 to 11.
The areas of two circles are in a ratio of 169:121. What is the ratio of their radii?
Answer:
[tex]1 \frac{48}{121} [/tex]
Step-by-step explanation:
divide 169/121 and that equals the answer above
Answer:
13 : 11
Step-by-step explanation:
If the ratio of radii = a : b, then
ratio of areas = a² : b²
Given
ratio of areas = 169 : 121, then
ratio of radii = [tex]\sqrt{169}[/tex] : [tex]\sqrt{121}[/tex] = 13 : 11
The population of United States is about 3×10(to the power of 8). The population of Kazakhstan is about 1.5×10(to the power of 7). How many times greater is the population of United States then Kazakhstan?
Answer:
The answer to your question is 20 times
Step-by-step explanation:
Data
United States' population = 3 x 10⁸
Kazakhstan's population = 1.5 x 10⁷
Process
1.- To solve this problem, just divide the United States' population by Kazakhstan's population.
3 x 10⁸ / 1.5 x 10⁷ = 20
2.- Conclusion
The population of the United States is 20 times greater than Kazakhstan's population.
Help please!!!!! Show work
Solve the equation
6(k+5)=66
Answer:
6
Step-by-step explanation:
6(k+5) = 6
k+5 = 66/6
k+5 = 11
k = 11-5
k = 6
What is the slope of the line whose equation is y−4= StartFraction 5 Over 2 EndFraction.(x−2)?
Answer:
m=5/2
Step-by-step explanation:
If [tex]y-4=\frac{5}{2}(x-2)[/tex], to find the slope, we first express the equation of the line in the slope-intercept form
y=mx+c, where
c=intercept on the y-axis
m=gradient/slope
[tex]y-4=\frac{5}{2}(x-2)\\y=\frac{5}{2}(x-2)+4\\y=\frac{5}{2}x-5+4\\y=\frac{5}{2}x-1[/tex]
Comparing with y=mx+c, the slope of the line, m=5/2
Answer:
5/2
Step-by-step explanation:
Karen started walking at 1 mile per hour. After she walked 2.5 miles, her friend Ned started walking along the same route at a piece of 1 mile per hour. If they continue to walk at the same rate, will Ned ever catch up to Karen? Explain.
Answer: No, Ned will never catch up to Karen.
Step-by-step explanation:
Karen started walking at 1 mile per hour.
Time = distance/speed
If she walks 2.5 miles, it means that the time she spent walking is
2.5/1 = 2.5 hours.
After she walked 2.5 miles, her friend Ned started walking along the same route at a speed of 1 mile per hour. Since Ned is walking at 1 mile per hour which is even slower than Karen's speed, it means that for every 1 mile that Ned walks, Karen walks 2.5 miles. Therefore, if
they continue to walk at the same rate, Ned will never catch up to Karen.
Some students in Springfield make a parade float with a letter S on it draw lines divide the shape into rectangles then find how many square feet the letter is
To find the square footage of the letter S on the parade float, the students can divide it into rectangles and calculate the area of each rectangle.
Explanation:The students can divide the shape of the letter S on the parade float into rectangles and then calculate the area of each rectangle to determine the total area of the letter. To do this, they can measure the length and width of each rectangle and multiply them together to find the area. Once they have the area of each rectangle, they can add them all together to get the total square footage of the letter S on the float.
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Megan invested in ten bonds of total face value of $1.000, issued by Zen Corporation. The bonds paid 10 percer semiannual (5% every 6 months) interest till the maturity date, which of the following is the value of interest earned in the first installment on a single bond? A) $50 B) $100 C) $500 D) $90 E) $75
Answer:
$50 is the value of interest earned in the first installment on a single bond
Step-by-step explanation:
Applying Interest earned in the first installment on a single bond ;
= PRT/100
P = $1.000
R = 5%
T = 1
Plugging the values in the equation ;
Interest = 1000 x 5 x 1 /100
= $50, hence option A is the correct one.
A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price.The customer was charged a 7% tax when the DVD was sold.What is the customer's total cost for the DVD?
Answer:
The customer's total cost for the DVD is $19.26
Step-by-step explanation:
Store buy the dvd for $12.00.
The store price is $12.00+50% more
The store price= $12.00 *(1+0.5)= $18.00
Final price (tax added)= $18.00 + 7%
Final price= $18.00 * (1 + 0.07)= $19.26
Answer:
The total cost of the DVD for the consumer was 19.26 $
Step-by-step explanation:
The sales price for the DVD was the price paid by the store plus 50%. To discover this value we will transform the percentage in a real number, by dividing it by 100, like following:
50/100 = 0.5
We then multiply this value by the price paid by the store (12) to find out how much is 50% of that. Then we add this value to the price paid by the store and we obtain the price of the DVD before taxes. So we do as following:
Price before taxes = price paid by the store + (price paid by the store)*0.5
Price before taxes = 12 + 12*0.5 = 18 $
On top of that there was 7% of tax for the consumer. We must repeat the same steps as before but using 7 instead of 50. So we have:
Final price = Price before taxes + (Price before taxes)*(7/100)
Final price = 18 + 18*0.07 = 19.26 $
The total cost of the DVD for the consumer was 19.26 $
In a poll conducted by a certain research center, 824 adults were called after their telephone numbers were randomly generated by a computer, and 10% were able to correctly identify the president. Identify the type of sampling used.
Answer:
Step-by-step explanation:
Hello!
Using a computer program 824 telephone numbers were randomly selected and a survey was conducted.
The sampling method used is the "simple random sampling" where the experimental units are randomly selected from the population without any kind of restriction and each unit has the same chance of being selected.
I hope it helps!
A tour bus normally leaves for its destination at 5:00 p.m. for a 200 mile trip. This week however, the bus leaves at 5:40 p.m. To arrive on time, the driver drives 10 miles per hour faster than usual. What is the bus’s usual speed?
Answer:
The usually speed of the bus is 50 miles/h.
Step-by-step explanation:
Let the usual speed of the bus be x mile/hour.
We know that
[tex]speed=\frac{distance}{time}[/tex]
[tex]\Rightarrow time = \frac{distance}{speed}[/tex]
The bus travels 200 miles.
To reach its destination it takes time [tex]=\frac{200}{x}[/tex] h
This week however the bus leaves at 5:40.
The bus late 40 minutes [tex]=\frac{40}{60} h[/tex] [tex]= \frac{2}{3}h[/tex]
Now the speed of the bus is = (x+10) miles/h
The new time to reach the destination is [tex]=\frac{200}{x+10}[/tex] h
According to the problem,
[tex]\frac{200}{x}-\frac{200}{x+10}=\frac{2}{3}[/tex]
[tex]\Rightarrow 200[\frac{x+10-x}{x(x+10)}]=\frac{2}{3}[/tex]
[tex]\Rightarrow 200[\frac{10}{x^2+10x}]=\frac{2}{3}[/tex]
⇒2(x²+10x)=200×10×3
⇒x²+10x = 3000
⇒x²+10x -3000=0
⇒x²+60x-50x-3000=0
⇒x(x+60)-50(x+60)=0
⇒(x+60)(x-50)=0
⇒x= -60,50
∴x=50 [since speed does not negative]
The usually speed of the bus is 50 miles/h.
The bus's usual speed is 60 mph.
To find the bus's usual speed, we can set up an equation based on the given information. Let the usual speed be x mph. Then, the time taken to travel 200 miles at the usual speed is 200/x. The time taken to travel the same distance at the increased speed (x+10) mph is 200/(x+10). Since the bus left late, these times should be equal, leading to the equation 200/x = 200/(x+10). Solving this equation, we find that x = 60 mph, which is the usual speed of the bus.
What kind of graph would be best to show the results of a group of students who were asked about their favorite kind of pizza. Explain your answer.
Answer:
A bar graph, because if you want to compare categories, you would want to categorize the results you get from a survey. If you were to use any other chart or graph, you would have to base it off of QUANTITATIVE data. Since this is QUALITATIVE data, it wouldn't make any sense to use any other chart or graph.
A bar graph is the best way to display categorical data such as the favorite kind of pizza.
What is the bar graph?A bar graph (also known as a bar chart) is a graphical representation of data that uses bars of different sizes. It is an excellent way of displaying relative sizes.
As per the question, a bar graph is the best way to display categorical data such as the favorite kind of pizza.
Each category (i.e., pepperoni, cheese, vegetarian, etc.) can be represented by a bar, with the height of the bar indicating the number or percentage of students who chose that category.
This allows for an easy visual comparison of the popularity of each kind of pizza.
Also, labels can be added to the x-axis and y-axis to provide additional information and context to the graph.
Therefore, a bar graph is an exact and effective way to present the data from the survey on students' favorite kinds of pizza.
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The number of students absent over two different days at Valley View Middle School can be represented as the sum 42 + 15. Which of these are equivalent representations of this sum? Choose all that are correct. Your answer: 5(8 + 2) + 5(3) (3 x 14) + (3 x 5) (3 x 39) + (3 x 5) 3(39 + 12) 3(14 x 5) 3(14 + 5)
Answer:
e) , f)
Step-by-step explanation:
42+15= 57
If the available options are:
a) 5(8+2)+5(3)=(5x10)+15=50+15=65
b) (3 x 14) + (3 x 5)= 42+15=57
c) (3 x 39) + (3 x 5)=117+15=132
d) 3(39 + 12)=3x51=153
e) 3(14 x 5)=3x70=210
f) 3(14 + 5)=3x19=57
Answer:
Step-by-step explanation:
simplify by dividing
3/5 ÷ -4/9
1. -27/20
2. 27/20
3. -12/45
4. 12/45
Answer:
The answer to your question is -27/20
Step-by-step explanation:
Divide 3/5 ÷ - 4/9
Process
1.- Just multiply the numerator of the first fraction by the denominator of the second fraction.
3 x - 9 = -27
2.- Multiply the denominator of the first fraction by the numerator of the second fraction.
5 x 4 = 20
3.- Join both results
-27/20
What is 6:12 in simplest form?
A.2
B.21
C. 12
D. 12.6
Answer:
It’s B
Step-by-step explanation:
Answer: 1:2 or 1/2
Step-by-step explanation:
6:12
Step 1: find a common divisible value, in this case, it is 6
Step2: divide through 6
1:2 or 1/2
Amber can paint a room in 20 hours. Christy can paint the same room in 16 hours. How long does it take for both amber and christy to paint the room if they are working together?
Answer: it will take them 8.89 hours
Step-by-step explanation:
Amber can paint a room in 20 hours. This means that Amber's working rate per hour is 1/20
Christy can paint the same room in 16 hours. This means that Christy's working rate per hour is 1/16
If they work together, they would be working simultaneously and their unit rates is additive. This means that their combined rate would be
1/20 + 1/16
Assuming it takes t hours for both of them to paint the room working together. It means that their combined working rate per hour is 1/t. Therefore
1/20 + 1/16 = 1/t
(16 + 20/320 = 1/t
36/320 = 1/t
t = 320/36
t = 8.89 hours
Amber and Christy can paint a room together in approximately 8.89 hours by combining their work rates. Each has individual work rates of 1/20 and 1/16, respectively, and their combined work rate is 9/80 of a room per hour.
To determine how long it will take for Amber and Christy to paint the room when working together, we can use the concept of combined work rates. First, we calculate each person's individual work rate. Amber's work rate is 1 room per 20 hours (1/20), and Christy's work rate is 1 room per 16 hours (1/16).
Adding their rates together gives us the combined work rate:
Combined rate = Amber's rate + Christy's rate
Combined rate = 1/20 + 1/16
To add these fractions, we need a common denominator, which in this case is 80:
Combined rate = (4/80) + (5/80) = 9/80
This means that together, Amber and Christy can paint 9/80 of the room per hour. To find the total time required to paint the entire room, we take the reciprocal of the combined work rate:
Total time = 1 / (Combined rate)
Total time = 1 / (9/80)
Total time = 80/9
Total time = 8.89 hours (rounded to two decimal places)
Therefore, Amber and Christy will be able to paint the room together in approximately 8.89 hours.
Sebastian gathered data by surveying his neighbors comparing how much time they spend on the internet to how much mail they receive in a week. Explain the steps Sebastian should take in order to analyze the data.
Step-by-step explanation:
1. The first is a tabulation of the data, in an organized, clear and concise way for each event.
2. After tabulation, for a better understanding of the data, statistical data, such as the mean, median, and standard deviation of each event, should be collected.
3. Finally, graph the data obtained to see the trend of both cases and thus have a very precise way to make the comparison of both events
LOGARITHMS, CONIC SECTIONS, SEQUENCES
Evaluating an exponential function with base e that models a real...
The number of milligrams D (n) of a drug in a patient's bloodstream h hours after the drug is injected is modeled by the following function.
D(h) =40e-0.5h
Find the initial amount injected and the amount in the bloodstream after 7 hours.
Round your answers to the nearest hundredth as necessary.
Initial amount:
milligrams
Amount after 7 hours:
milligrams
X
5
?
Explanation
Check
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Answer:
(a) 40 milligrams
(b) 1.21 milligrams
Step-by-step explanation:
Exponential Function
It's commonly used to model real situations in life, like this one proposed in the question where the number of milligrams of a drug D(h) in a patient's bloodstream h hours after the drug is injected is modeled by the following function.
[tex]D(h) =40e^{-0.5h}[/tex]
(a) The initial amount injected to the patient can be found when h=0
[tex]D(0) =40e^{-0.5(0)}=40e^{0}=40[/tex]
Initial amount: 40 milligrams
(b) Let's plug h=7
D(7) =40e^{-0.5(7)}=40e^{-3.5}=1.21
The amount in the bloodstream after 7 hours is 1.21 milligrams
List the first twenty counting numbers in the indicated base below. twelve (Only digits 0, 1, 2, 9, A, B are used in base twelve.) What are the first twenty counting numbers in base twelve? (Use a comma to separate answers as needed.)
Answer:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13, 14, 15, 16, 17, 18
Step-by-step explanation:
The first twenty counting numbers in base ten are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. If we convert each of these numbers to base twelve, then we will get the first twenty counting numbers in base twelve. We now proceed with the conversion below.
The first twelve digits of base 12 are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B.
12 in base 10 = 10 in base 12 since 12/12 = 1 R 0.
13 in base 10 = 11 in base 12 since 13/12 = 1 R 1.
14 in base 10 = 12 in base 12 since 14/12 = 1 R 2.
15 in base 10 = 13 in base 12 since 15/12 = 1 R 3.
16 in base 10 = 14 in base 12 since 16/12 = 1 R 4.
17 in base 10 = 15 in base 12 since 17/12 = 1 R 5.
18 in base 10 = 16 in base 12 since 18/12 = 1 R 6.
19 in base 10 = 17 in base 12 since 19/12 = 1 R 7.
20 in base 10 = 18 in base 12 since 20/12 = 1 R 8.
So the next 8 counting numbers of base 12 are 10, 11, 12, 13, 14, 15, 16, 17, 18.
The student requested the first twenty numbers in the base twelve system. In this system, the digits 0 to 9 are used as in decimal, but 'A' represents ten and 'B' represents eleven. The sequence starts with 0 and follows with 1, 2, ... 9, A, B, 10 (twelve in decimal), up to 17 (nineteen in decimal).
The student asked for the first twenty counting numbers in base twelve, also known as the duodecimal system. In this system, we use the digits 0, 1, 2, ..., 9, A, and B, where A represents ten and B represents eleven in decimal. Here is the list:
0123456789AB1011121314151617After the number B, the numbers continue with 10 (equivalent to twelve in decimal), then 11 (thirteen), and so on until 17, which is nineteen in decimal.
Out of 3000 light bulbs that were tested, 126 were defective. find the prbability of defective and non defective
Answer:
P(defective) = 126/3000 = 0.042
P(not defective) = 1 - P(defective)
= 1 - 0.042 = 0.958
An employee compiled sales data for a company once each month. The scatter plot below shows the sales (in multiples of $1000) for the company over time (in months). The equation represents the linear model for this data. y = 0.94x + 12.5 According to the model, how much do the company's sales increase per month? $9400 $940 $1250 $12,500 $5000
Answer:
Option B) $940
Step-by-step explanation:
We are given the following in the question:
[tex]y = 0.94x + 12.5[/tex]
The equation represents the company sales in thousand dollars and x is time in months.
Comparing to general form of linear equation.
[tex]y = mx + c[/tex]
Comparing, we get,
Slope, m = 0.94
y-intercept, c = 12.5
Interpretation:
Thus, the slope tells us the increase in sales of company with one unit increase in x that is it tells the increase in company's sale per month.
[tex]0.94\times 1000 = 940[/tex]
$940 is the increase in company's sale per month.
Option B) $940
Answer:
B 940
Step-by-step explanation:
Tina bake some cookies 1/2 of her cookies with peanut butter 1/2 of the peanut butter cookies also have chocolate chips what fraction of the cookies were peanut butter and have chocolate chips
Answer: 1/4
Step-by-step explanation:
so if 1/2 of 1/2 of cookies are with choclate chips therefore saying 1/2 cookies is the same as 2/4 cookies and since half of the cookies are with choclate chips so there are 1/4 cookies with choclate chips nd are peanut butter please mark brainliest.
Answer:1/4
Step-by-step explanation: Half of the cookies baked were peanut butter cookies. 1/2 of the peanut butter cookies have chocolate chips. 1/2 divided by 1/2 is 1/4. 1/4 of the total cookies baked are peanut butter chocolate chip cookies.
Find a. If necessary, round your answer to the nearest hundredth.
Sorry the picture was upside down. :(
Answer:
The answer to your question is a = 4.81
Step-by-step explanation:
Process
1.- The angle B and 43° are supplementary
B + 43° = 180°
B = 180 - 43
B = 137°
2.- Calculate angle C
The sum of the internal angles in a triangle equals 180°
A + B + C = 180°
29 + 137 + C = 180
- Solve for C
C = 180 - 29 - 137
C = 14°
3.- Use the law of signs to find a
a / sin A = c / sin C
a / sin 29 = 2.4 / sin 14
- Solve for a
a = 2.4 sin 29 / sin 14
- Simplification
a = 2.4 (0.485) / 0.242
- Result
a = 4.809
Jerome took $20 to the store to buy a book and some CDs. If he buys a book that costs $4.50, write an inequality to find the most he could spend on CDs.
Answer:
y[tex]\leq[/tex]15.5
Step-by-step explanation:
The Total Amount taken to the store by Jerome = $20
He buys a book worth $4.50
Let y be the most he could spend on CDs
Since he is spending on books and CDs, the amount spent cannot be more than total sum he has, therefore:
y+$4.50[tex]\leq[/tex]20
This is because he could spend either less than $20 or exactly $20
y[tex]\leq[/tex]20-4.50
y[tex]\leq[/tex]15.5 is the inequality to find the most he could spend on CDs.
) One year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million. Suppose a sample of 400 major league players was taken. Find the approximate probability that the average salary of the 400 players exceeded $1.1 million.
Answer:
Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.
Step-by-step explanation:
We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.
Suppose a sample of 400 major league players was taken.
Let [tex]\bar X[/tex] = sample average salary
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean salary = $1.5 million
[tex]\sigma[/tex] = standard deviation = $0.9 million
n = sample of players = 400
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P([tex]\bar X[/tex] > $1.1 million)
P([tex]\bar X[/tex] > $1.1 million) = P( [tex]\frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }[/tex] > [tex]\frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} }[/tex] ) = P(Z > -8.89) = P(Z < 8.89)
Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.
Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.
The approximate probability that the average salary of the 400 players exceeded $1.1 million will be "1".
ProbabilityAccording to the question,
Standard deviation, σ = 0.9
Mean, μ = 1.5
Let,
The salaries for professional sports player be "x".
Now,
The probability will be:
= P ([tex]\bar x[/tex] > 1.1)
= P ([tex]\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{1.1 - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex])
By substituting the values,
= P (Z > [tex]\frac{1.1 -1.5}{\frac{0.9}{\sqrt{400} } }[/tex])
= P (Z > -8.89)
By using the table,
= 1
Thus the above answer is correct.
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At the zoo there are two different tours. One leaves every 30 minutes and one leaves every 45 minutes. If they both leave at 8:00am, at what time will they be the same again
The two zoo tours start at 8:00 am, one leaves every 30 minutes and the other every 45 minutes. The next time they will coincide, or leave at the same time, is at 9:30 am.
Explanation:The tours in the zoo that are mentioned in your question represent two different intervals, 30 minutes and 45 minutes. To figure out when these tours will coincide again, we actually need to find a common multiple of the two intervals. The smallest common multiple of 30 and 45 minutes is 90 minutes or 1 hour and 30 minutes.
So, if both tours start at 8:00 am, they will sync again 90 minutes later, which is 9:30 am. Therefore, the two tours will depart together again at 9:30 am.
Learn more about Time Intervals here:https://brainly.com/question/4579013
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Factor the expression. 35g^2 – 2gh – 24h^2
(7g + 6)(5g + 4h2)
(7g + 6h)(5g – 4h)
(7g – 6h)(5g + 4h)
(7g – 6)(5g + 4)
Option C: [tex](7 g-6 h)(5 g+4 h)[/tex] is the correct answer.
Explanation:
The given expression is [tex]35 g^{2}-2 g h-24 h^{2}[/tex]
We need to determine the factor of the expression.
Now, let us break the given expression into two groups.
Hence, we get,
[tex]35 g^{2}+28 g h-30 g h-24 h^{2}[/tex]
Simplifying, we get,
[tex]\left(35 g^{2}+28 g h\right)+\left(-30 g h-24 h^{2}\right)[/tex]
Let us factor out 7g from the term [tex]\left(35 g^{2}+28 g h\right)[/tex]
Hence, we have,
[tex]7 g(5 g+4 h)+\left(-30 g h-24 h^{2}\right)[/tex]
Similarly, let us factor out -6h from the term [tex]\left(-30 g h-24 h^{2}\right)[/tex]
Thus, we have,
[tex]7 g(5 g+4 h)-6 h(5 g+4 h)[/tex]
Now, we shall factor out the term [tex]5g+4h[/tex] , we get,
[tex](7 g-6 h)(5 g+4 h)[/tex]
Thus, the factorization of the given expression is [tex](7 g-6 h)(5 g+4 h)[/tex]
Therefore, Option C is the correct answer.
Answer:
Option C is the correct answer.
Step-by-step explanation: